Mathematical set operations in Java / searching for library

[mowsen]

Dear Group,


i'm searching for a Java library which supports all ways of set
handling, like generating a set of all prime numbers up to 10000, diff
it to another set and so on.

Anyone a hint?

Thanks,
mowsen

 

[Roedy Green]

i'm searching for a Java library which supports all ways of set
handling, like generating a set of all prime numbers up to 10000, diff
it to another set and so on.

see http://mindprod.com/jgloss/enumset.html
http://mindprod.com/jgloss/binary.html#BITSET
http://mindprod.com/products2.html#PRIMES

 

[Robert Klemme]

i'm searching for a Java library which supports all ways of set
handling, like generating a set of all prime numbers up to 10000, diff
it to another set and so on.

java.util.Set and implementors. Google will yield plenty of prime
number generation algorithms.

robert

 

[mowsen]

thanks. i'm not quite sure, but is it possible to define for example
all natural numbers easily with enumset/set?!

thanks,
moka

 

[Eric Sosman]

thanks. i'm not quite sure, but is it possible to define for example
all natural numbers easily with enumset/set?!

If you can afford that much memory, I want to be your friend.

 

[Bent C Dalager]

thanks. i'm not quite sure, but is it possible to define for example
all natural numbers easily with enumset/set?!

No. One reason is that the interface java.util.Set<E> requires you to
implement:

int size() - Returns the number of elements in this set (its
cardinality).

And the int data type does not define a bit pattern that means
"infinite". You could therefore not implement an infinite size set
(such as N) using java.util.Set while honouring the interface
requirements for that type.

Cheers,
Bent D

 

[Robert Klemme]

thanks. i'm not quite sure, but is it possible to define for example
all natural numbers easily with enumset/set?!

You did not mention infinite sets in your original posting...

I don't know what you intend to do but maybe a math system like
mathematica and similar is better suited to your needs. There are even
free implementations available.

Cheers

robert

 

[Stefan Ram]

thanks. i'm not quite sure, but is it possible to define for
example all natural numbers easily with enumset/set?!

The set of all Java Integer objects (just written - never
compiled, so there will still be errors, but you get the idea):

class Integers extends java.util.AbstractSet implements java.util.Set
{ public Integers(){} @java.lang.Override
public void clear(){ throw new java.lang.UnsupportedOperationException; }
@java.lang.Override public boolean contains( final java.lang.Object key )
{ return java.lang.Integer.class.isAssignableFrom( key.getClass()); }
@java.lang.Override public boolean remove( final java.lang.Object key )
{ throw new java.lang.UnsupportedOperationException; }
@java.lang.Override public int size()
{ return java.lang.Integer.MAX_VALUE; }
@java.lang.Override public boolean add( final java.lang.Object arg0 )
{ throw new java.lang.UnsupportedOperationException; }
@java.lang.Override public java.util.Iterator iterator()
{ return new java.util.Iterator()
{ int i = java.lang.Integer.MIN_VALUE;
public boolean hasNext(){ return i + 1 > i; }
public java.lang.Object next(){ return ++i; } public void remove()
{ throw new java.lang.UnsupportedOperationException; }}}}

Mathematical integers can not all be represented as distinct
objects or values by a computer, because they are not limited
in size, so a storage for a single mathematical integer value
would need to have more states the possible different states
of our whole universe. This also holds for storages of sets of
mathematical integers.

 

[Daniel Pitts]

The set of all Java Integer objects (just written - never
compiled, so there will still be errors, but you get the idea):

class Integers extends java.util.AbstractSet implements java.util.Set
{ public Integers(){} @java.lang.Override
public void clear(){ throw new java.lang.UnsupportedOperationException; }
@java.lang.Override public boolean contains( final java.lang.Object key )
{ return java.lang.Integer.class.isAssignableFrom( key.getClass()); }
@java.lang.Override public boolean remove( final java.lang.Object key )
{ throw new java.lang.UnsupportedOperationException; }
@java.lang.Override public int size()
{ return java.lang.Integer.MAX_VALUE; }
@java.lang.Override public boolean add( final java.lang.Object arg0 )
{ throw new java.lang.UnsupportedOperationException; }
@java.lang.Override public java.util.Iterator iterator()
{ return new java.util.Iterator()
{ int i = java.lang.Integer.MIN_VALUE;
public boolean hasNext(){ return i + 1 > i; }
public java.lang.Object next(){ return ++i; } public void remove()
{ throw new java.lang.UnsupportedOperationException; }}}}

Mathematical integers can not all be represented as distinct
objects or values by a computer, because they are not limited
in size, so a storage for a single mathematical integer value
would need to have more states the possible different states
of our whole universe. This also holds for storages of sets of
mathematical integers.

While the statement is true, the representation of infinite sets can be
accomplished in finite space. You only need to abstract the behavior of
such a set.

For instance, setOfPrimes.intersect(setOfEvenNumbers) would be equal to
the set that contains "2".

While, I wouldn't want to write the implementation of those objects, it
is a feasible undertaking if you add appropriate restrictions on the
number of different types of sets you could do.

Also, if you can create a formula to iterate or calculate certain
properties of the set, then you needn't represent all the values in the set.

in setOfEvenNumbers:
public boolean contains(Integer o) {
return o.intValue() % 2 == 0;
}

You might build an abstract interface to mathematical sets that is
different than the Java "Set" interface, as generally in Mathematics,
you specify rules, conditions, relationships, etc. for inclusion in a
set, rather than adding individual elements. Java Collections are very
specifically designed to "hold" collections of Java Objects, not
mathematical abstractions.

There may or may not be such a library already created. I would google
for it before discounting the possibility.

Good luck,
Daniel.

 

[Stefan Ram]

you specify rules, conditions, relationships, etc. for inclusion in a

This is also known as »symbolic mathematics«
in contrast to »numerical mathematics«.

There may or may not be such a library already created.
I would google for it before discounting the possibility.

Or even use an old-fashioned catalogue, such as:

http://www.google.com/Top/Science/Math/Software/

(Including some Java software or libraries.)

 

[Stefan Ram]

i'm searching for a Java library which supports all ways of set
handling, like generating a set of all prime numbers up to 10000, diff
it to another set and so on.

The efficient implementation depends on knowledge
of implementation and expected usage (calls).

A SetDiff, for example, could be done as

.... class DiffSet ...
{ public Diff( final java.util.Set a, final java.util.Set b ) ...

public boolean contains( final java.lang.Object o )
{ return a.contains( o )&& !b.contains( o ); }

public java.util.Iterator iterator()
{ ... /* Use the iterator of a, skipping when b.contains( ... ) */ ... }

A well-known DSL for set operations is SQL.

 

[Lew]

A SetDiff, for example, could be done as

.... class DiffSet ...
{ public Diff( final java.util.Set a, final java.util.Set b ) ...

public boolean contains( final java.lang.Object o )
{ return a.contains( o )&& !b.contains( o ); }

public java.util.Iterator iterator()
{ ... /* Use the iterator of a, skipping when b.contains( ... ) */ ... }

A well-known DSL for set operations is SQL.

Another way to handle diffs:

public static <T> Set <T> diff( Set<? extends T> a, Set<? extends T> b )
{
Set <T> diff = new HashSet <T> ( a );
diff.removeAll( b );
return diff;
}

If you don't mind changing the contents of 'a', youi can skip the wrapper
method and just use a.removeAll( b ).